Finding values of x where the infinite geometric series converge

[meeklobraca]

1. The problem statement, all variables and given/known data
(2+x)+(2+x)^2+(2+x)^3 + ....


2. Relevant equations





3. The attempt at a solution

Ive found that the l r l < 1

the r of this equation is (2 + x)

so we have -1 < 2 + x < 1

The values of x where the series coverges is -3 < x < -1

Is this correct?

Thanks!

[tiny-tim]

(2+x)+(2+x)^2+(2+x)^3 + ....
…
Ive found that the l r l < 1

the r of this equation is (2 + x)

so we have -1 < 2 + x < 1

The values of x where the series coverges is -3 < x < -1

Is this correct?

Thanks!

:rofl: :rofl: :rofl: :rofl:

Hint: does it converge for x = 0? :wink:

[gabbagabbahey]

1. The problem statement, all variables and given/known data
(2+x)+(2+x)^2+(2+x)^3 + ....


2. Relevant equations





3. The attempt at a solution

Ive found that the l r l < 1

the r of this equation is (2 + x)

so we have -1 < 2 + x < 1

The values of x where the series coverges is -3 < x < -1

Is this correct?

Thanks!

Looks good to me:approve:

[meeklobraca]

:rofl: :rofl: :rofl: :rofl:

Hint: does it converge for x = 0? :wink:



No I dont think so?

Does your laughing faces mean I got it right? lol

[tiny-tim]

No I dont think so?

Does your laughing faces mean I got it right? lol

oh dear … I read a -1 as a 1. :redface:

Yes … sorry, meeklobraca … you got it right! :biggrin: